AbstractThis paper develops a framework for analyzing the impact of macroeconomic conditions on creditrisk and dynamic capital structure choice. We begin by observing that when cash ows depend oncurrent economic conditions, there will be a benet for rms to adapt their default and nancing policiesto the position of the economy in the business cycle phase. We then demonstrate that this simpleobservation has a wide range of empirical implications for corporations. Notably, we show that ourmodel can replicate observed debt levels and the countercyclicality of leverage ratios. We alsodemonstrate that it can reproduce the observed term structure of credit spreads and generate strictlypositive credit spreads for debt contracts with very short maturities. Finally, we characterize the impactof macroeconomic conditions on the pace and size of capital structure changes, and debt capacity.r 2006 Elsevier B.V. All rights reserved.JEL classification: G12; G32; G33Keywords: Dynamic capital structure; Credit spreads; Macroeconomic conditions

D. Hackbarth et al. / Journal of Financial Economics 82 (2006) 519550

1. IntroductionSince Modigliani and Miller (1958), economists have devoted much effort tounderstanding rms nancing policies. While most of the early literature analyzesnancing decisions within qualitative models, recent research tries to provide quantitativeguidance as well.1 However, despite the substantial development of this literature, littleattention has been paid to the effects of macroeconomic conditions on credit risk andcapital structure choices. This is relatively surprising since economic intuition suggests thatthe economys business cycle phase should be an important determinant of default risk,and thus, of nancing decisions. For example, we know that during recessions, consumersare likely to cut back on luxuries, and thus rms in the consumer durable goods sectorshould see their credit risk increase. Moreover, there is considerable evidence thatmacroeconomic conditions impact the probability of default (see Fama, 1986; Dufe andSingleton, 2003, pp. 4547). Yet, existing models of rms nancing policies typicallyignore this dimension.In this paper we contend that macroeconomic conditions should have a large impact notonly on credit risk but also on rms nancing decisions. Indeed, if one determines optimalleverage by balancing the tax benet of debt and bankruptcy costs, then both the benetand the cost of debt should depend on macroeconomic conditions. The tax benet of debtobviously depends on the level of cash ows, which in turn should depend on whether theeconomy is in an expansion or in a contraction. In addition, expected bankruptcy costsdepend on the probability of default and the loss given default, both of which shoulddepend on the current state of the economy. As a result, variations in macroeconomicconditions should induce variations in optimal leverage.The purpose of this paper is to provide a rst step towards understanding thequantitative impact of macroeconomic conditions on credit risk and capital structuredecisions. To do so, we develop a contingent claims model in which the rms cash owsdepend on both an idiosyncratic shock and an aggregate shock that reects the state of theeconomy. The analysis is developed within a standard model of capital structure decisionsin the spirit of Mello and Parsons (1992). Specically, we consider a rm that has exclusiveaccess to a project that yields a stochastic stream of cash ows. The rm is levered becausedebt allows it to shield part of its income from taxation. However, leverage is limitedbecause debt nancing increases the likelihood of costly nancial distress. Once debt hasbeen issued, shareholders have the option to default on their obligations. Based on thisendogenous modeling of default, the paper derives valuation formulas for coupon-bearing

debt with arbitrary maturity, equity, and levered rm value. We then use these closed-formexpressions to analyze credit risk and determine optimal leverage.The analysis shows that, when the value of the aggregate shock shifts between differentstates (boom or recession), the shareholders default policy is characterized by a differentdefault threshold for each state. Under this policy the state space can be partitioned intovarious domains including a continuation region in which no default occurs. Outside of thisregion, default can occur either because cash ows reach the default threshold in a givenstate or because of a change in the state of the aggregate shock. In other words, aggregateshocks generate some time-series variation in the present value of future cash ows tocurrent cash ows that may induce the rm to default following a change inmacroeconomic conditions. The paper also demonstrates that while variationsin idiosyncratic shocks are unlikely to explain the clustering of exit decisions observedin many markets, changes in macroeconomic conditions provide the basis for suchphenomena.Following the analysis of the shareholders default policy, we examine the implicationsof the model for nancing decisions. The leverage ratios that the model generates are inline with those observed in practice. In addition, the model predicts that leverage iscountercyclical, consistent with the evidence reported by Korajczyk and Levy (2003). Wealso examine dynamic capital structure choice and relate both the pace and the size ofcapital structure changes to macroeconomic conditions.2 In particular, we nd that rmsshould adjust their capital structure more often and by smaller amounts in booms than inrecessions. Another quantity of interest for corporations is the credit spread on corporatedebt. We show that the model can generate a term structure of credit spreads that is in linewith empirically observed credit spreads on corporate debt and strictly positive creditspreads for short term debt issues.The remainder of the paper is organized as follows. Section 2 develops a static model ofcapital structure decisions in which rms cash ows depend on macroeconomicconditions. Section 3 determines the prices of corporate securities. Section 4 discussesimplications. Section 5 examines dynamic capital structure choice. Section 6 concludes.

The study by Drobetz and Wanzenried (2004) provides early empirical support for this hypothesis.Throughout the analysis, the risk free rate r is constant and, as a result, does not move with macroeconomicconditions. This is supported by the weak historical correlation (presumably due to adjustments in monetarypolicy) between uctuations in real GDP or uctuations in real consumption and the rate of return on risk-freedebt. More specically, over the period 1959:3 to 1998:4, the correlation between the quarterly growth rate on realconsumption per capita (source: NIPA on non durables and services) and the three-month T-bill rate on thesecondary market is -0.0031. Over that same period, the correlation between the quarterly growth rate on GDPand the three-month T-bill rate on the secondary market is 0.0561. In addition, Campbell (1999) reports that thethe annualized standard deviation of the ex post real returns on U.S. Treasury bills is 1.8% and much of this isdue to short-term ination risk. [...] Thus, the standard deviation of the ex ante real interest rate is considerablysmaller.3

ARTICLE IN PRESS522

D. Hackbarth et al. / Journal of Financial Economics 82 (2006) 519550

continuous and uncertainty is modeled by a complete probability space O; F; P. We

consider an innitely-lived rm with assets that generate a continuous stream of cash ows.Management acts in the best interests of shareholders. Corporate taxes are paid at a rate ton operating cash ows, and full offsets of corporate losses are allowed. At any time t, therms instantaneous operating prot (EBIT) satises:f xt ; yt xt yt ,

(1)

where yt tX0 is an aggregate shock that reects the state of the economy, and xt tX0 is anidiosyncratic shock that reects the rm-level productivity uncertainty.4 We presume thatxt tX0 is independent of yt tX0 and evolves according to the geometric Brownian motion:dxt mxt dt sxt dW t ;

x0 40 given,

(2)

where mor and s40 are constant parameters and W t tX0 is a standard Brownian motiondened on O; F; P. Both x and y are observable to all agents.Because the rm pays taxes on corporate income, it has an incentive to issue debt.Following Leland (1998), we consider nite-maturity debt structures in a stationaryenvironment. The rm has debt with constant principal p and paying a constant totalcoupon c at each moment in time. It instantaneously rolls over a fraction m of its totaldebt. That is, the rm continuously retires outstanding debt principal at a rate mp (exceptwhen bankruptcy occurs), and replaces it with new debt vintages of identical coupon,principal, and seniority. Therefore, any nite-maturity debt policy is completelycharacterized by the tuple c; m; p. In the absence of bankruptcy, the average debtmaturity T equals 1=m.Economically, our nite-maturity debt assumption corresponds to commonly usedsinking fund provisions (e.g., Smith and Warner, 1979). Mathematically, this modelingapproach is equivalent to debt amortization being simply an exponential function of time.Since the total coupon rate and the sinking fund requirement are xed, we obtain a timehomogeneous setting akin to Leland (1998), Dufe and Lando (2001), and Morellec(2001). We further assume that the debt coupon is initially determined such that debt valueequals principal value. That is, debt is issued at par.5 Proceeds from the debt issue are paidout as a cash distribution to shareholders at the time of otation.Once debt has been issued, shareholders only decision is to select the default policy thatmaximizes equity value. We presume that if the rm defaults on its debt obligations, it isimmediately liquidated. In the event of default, the liquidation value of the rm is aAxt ,where a 2 0; 1 is a regime-dependent recovery rate on assets and Axt is the value ofunlevered assets. Section 5 extends the basic model to incorporate dynamic capitalstructure choice. In this more general setting, shareholders have to decide on the initialamount of debt to issue as well as the optimal default and restructuring policies.Suppose that the rms production function is Y t At N gt ; where Y t is output, At is the rm-level productivityshock, N t is labor, and g 2 0; 1 represents returns to scale. Let the inverse demand function be given by1=ept ht Y t , where ht represents the aggregate demand shock and e40 is the elasticity of demand. Then therms prot is given by f t maxN t pt Y t wt N t , where wt is the wage rate, which is assumed to be constant.1=1y 1=g y=1y1=1ySolving yields f t yy=1y 1 yhtAt w twith y ge 1=e. Letting yt yy=1y 1 yhtand1=g y=1yxt At wt, we obtain f t xt yt as in Eq. (1).5This assumption implies that the tax benets of debt only hinge upon the chosen debt coupon and hence do notdepend on whether debt is initially oated at a discount or premium to principal value.4

2.2. Relation with existing literature

Before proceeding to the analysis, it might be helpful to briey contrast the presentmodel with some related lines of research.Contingent claims analysis. As in previous contingent claims models, we analyze equityin a levered rm as an option on the rms assets and model the decision to default as astopping problem. The distinguishing feature of our model is that the current cash owdepends on current macroeconomic conditions (expansion or contraction). Because thedecision to default balances the present value of cash ows in continuation with the presentvalue of cash ows in default, this implies that the decision to default also depends oncurrent macroeconomic conditions. This feature is unique to our model and cannot bereproduced by introducing discontinuities through a jump-diffusion model.Regime shifts and firms policy choices. Recent work by Guo et al. (GMM, 2005)investigates the impact of discrete changes in the growth rate and volatility of cash ows onrms investment decisions. One important point of departure from GMM is that weintroduce regime shifts in the aggregate shock only and the aggregate shock inuences cashows multiplicatively. Another important difference is that GMM analyze real investmentwhereas we examine capital structure decisions. Finally, from a technical point of view,GMM solve a control problem in which control policies change the underlying diffusionprocess whereas we solve a stopping problem.3. Valuation of corporate securitiesIn this section, we derive the values of corporate debt and equity as well as the defaultthresholds selected by shareholders. These results will be used below to analyze credit riskand capital structure decisions. To examine the impact of macroeconomic conditions onthese quantities in the simplest possible environment, we assume that the aggregate shockyt tX0 can only take two values: yL and yH with yH 4yL 40. In addition, we presume thatyt is observable and that its transition probability follows a Poisson law, such that yt tX0 isa two-state Markov chain. Let li 40 denote the rate of leaving state i and i denote thetime to leave state i. Within the present model, the exponential law holds:Pi 4t eli t ;

i H; L,

(3)

and there is a probability li Dt that the value of the shock yt tX0 changes from yi to yjduring an innitesimal time interval Dt. In addition, the expected duration of regime L islL 1 and the average fraction of time spent in that regime is lH lL lH 1 .3.1. Finite-maturity debt valueWe start by determining the value of corporate debt. Debt value equals the sum of thepresent value of the cash ows that accrue to debtholders until the default time and thechange in this present value that arises in default. Since the latter component depends onthe rms abandonment value, we start by deriving this value.3.1.1. Abandonment valueWe follow Mello and Parsons (1992) and Leland (1994) by presuming that theabandonment value of the rm equals the value of unlevered assets, i.e., the unlimited

liability value of a perpetual claim to the current ow of after-tax operating income.

Denoting by E P j the conditional expectation operator associated with P, we can thuswrite this value as

Z 1

Ai x E Pert 1 txt yt dtx0 x; y0 yi ; i L; H.(4)0

Since the level of the rms operating cash ows depend on the current regime, so does therms abandonment value. Applying Itos lemma and simplifying, we nd that Ai xsatises the system of ordinary differential equations (ODEs):s2 2 00x AL x lL AH x AL x 1 txyL ,52s26rAH x mxA0H x x2 A00H x lH AL x AH x 1 txyH .2Within the current framework, the expected rate of return on corporate securities is r.Thus, the left-hand side of these equations reects the required rate of return for holdingthe asset per unit of time. The right-hand side is the expected change in the asset value (i.e.,the realized rate of return). These expressions are similar to those derived in standardcontingent claims models. However, they contain the additional term li Aj x Ai x,which reects the impact of the aggregate shock on the value functions. This term is theproduct of the instantaneous probability of a regime shift and the change in the valuefunction occurring after a regime shift.Solving these ODEs subject to the boundedness conditionsrAL x mxA0L x

lim

x!1

Ai xo1x

and

lim Ai xo1

x!0

(7)

yields the following expression for the rms abandonment value:

Ai x 1 tK i x;

i L; H,

(8)

whereyHlH yH yL

,r m r mr m lL lH yLlL yH yL KL

.r m r mr m lL lH

KH

910

In the above two expressions, the rst term on the right hand side is the abandonmentvalue of the rm in the absence of regime shifts. The second term adjusts this abandonmentvalue to reect the possibility of a regime shift (thereby attenuating implied changes).3.1.2. Debt valueConsider next the value of corporate debt. Denote by d 0i x; c; m; p; t the date t valueof debt issued at time 0. These original debtholders receive a total payment rate ofemt c mp as long as the rm is solvent. Now dene the value of total outstanding debtat any date t by d i x; c; m; p emt d0i x; c; m; p; t. Because d i x; c; m; p receives a constantpayment rate c mp, it is independent of t.Let xi denote the default threshold that maximizes equity value in regime i H; L.Since f is strictly increasing in y and yL oyH , it is straightforward to show that xL 4xH .

That is, the rm defaults earlier in recessions than in expansions. Using Itos lemma, it canbe shown that the total value of outstanding debt solves the following system of ODEs (thearguments for the debt structure c; m; and p are omitted):

In the region xH pxpxL ,

r md H x mxd 0H x

s2 2 00x d H x lH aL AL x d H x c mp.2(11)

In the region xXxL ,

As is the case for the abandonment value, these equations are similar to those obtainedin the standard diffusion case (e.g., Leland, 1998), and they incorporate an additional termthat reects the impact of the possibility of a change in the value of the aggregate shock onasset prices. This term equals lH aL AL x d H x in Eq. (11), where aL is the recoveryrate in a recession, since it will be optimal for shareholders to default subsequent to achange of yt from yH to yL on the interval xH ; xL . (See Section 3.3.2 for a discussion.)This system of ODEs is associated with the following four boundary conditions:d L xL ; c; m; p aL AL xL ,d H xH ; c; m; p

14

aH AH xH ,

lim d H x; c; m; p lim d H x; c; m; p,

1516

lim d 0H x; c; m; p lim d 0H x; c; m; p,

17

x#xL

x"xL

x#xL

x"xL

where derivatives are taken with respect to x. The value-matching (14)(15) impose an equalitybetween the value of corporate debt and the value of cash ows accruing to debtholders indefault. Because the decision to default does not belong to bondholders, these value-matchingconditions are not associated with additional optimality conditions. In addition, because cashows to claimholders are given by a (piecewise) continuous Borel-bounded function, the debtvalue functions d i are piecewise C2 (see Theorem 4.9, pp. 271 in Karatzas and Shreve, 1991).Therefore, the value function d H is C0 and C1 and satises the continuity and smoothness(16)(17). Solving Eqs. (12)(17), we obtain the following proposition, where, for notationalconvenience, we identify nite-maturity debt parameters by bars (e.g., x or T).Proposition 1. When the firms operating cash flows are given by Eq. (1) and it has issuedfinite-maturity debt with coupon payment c, instantaneous debt retirement rate m, and totalprincipal p, the value of corporate debt in regime i L; H is given by8< Axx lL Bxg c mp; xXx ;Lrm(18)d L x; c; m; p : a 1 tK x;xpx ;L

value of corporate debt is equal to the sum of the value of a perpetual entitlement to thecurrent debt service ow and the change in value that occurs either after a sudden changein the value of the aggregate shock or when the idiosyncratic shock smoothly reaches adefault boundary xi . In these valuation formulas, the default threshold is determined byshareholders and hence is an exogenous parameter for bondholders.Proposition 1 shows that the value of corporate debt in the continuation region xL ; 1has three components. First, it incorporates the value of a perpetual claim to the stream ofrisk-free coupon and debt retirement payments. Second, it reects the change in valuearising when the idiosyncratic shock reaches the default boundary xL from above for therst time; i.e., debtholders recoveries. Third, it captures the change in default risk thatoccurs following a change in the value of the aggregate shock. The value of corporate debtin the transient region xH ; xL also has three components. First, it includes the value of aperpetual claim to the stream of non defaultable debt payments, c mp=r lH m.Because the rate of leaving state i H is lH , the discount rate is increased by lH to reectthe possibility of a change in the value of the aggregate shock. Second, it reects the changein debt value that arises when the value of the idiosyncratic shock either reaches thedefault boundary xH the rst time from above or the upper boundary of that region xLfrom below. Third, it captures the change in value that arises when default occurs suddenly(i.e., following a change of yt from yH to yL on the interval xH ; xL ).3.2. Firm valueWe now turn to the value of the levered rm. Total rm value equals the sum of theunlimited liability value of a perpetual claim to the current ow of after-tax operating income,plus the present value of a perpetual claim to the current ow of tax benets of debt, minusthe change in those present values arising in default. Thus, the levered rm value vi x satisesthe following system of ODEs (the argument for the coupon c is omitted):

The expressions reported in Proposition 2 for the levered rm value are similar to thoseprovided for the value of corporate debt (Proposition 1) and, thus, admit a similarinterpretation. Total rm value is equal to the sum of the value of a perpetual entitlementto the current ow of income and the change in value that occurs either after a change in

the value of the aggregate shock or when the idiosyncratic shock reaches a boundary xi .As was the case for the value of corporate debt, the default threshold is chosen solely byshareholders and hence is an exogenous parameter for rm value.3.3. Equity value and default policyBecause the values of corporate securities depend on the default threshold selected byshareholders, we now turn to the valuation of equity. Based on the closed-form solutionfor equity value, we will derive the equity value-maximizing default policy.3.3.1. Equity valueIn the absence of arbitrage, levered rm value equals the sum of the debt and equityvalues. Formally, vi d i ei for i L; H. This simple observation permits thefollowing result.Proposition 3. When the firms operating cash flows are given by Eq. (1) and the firm hasissued finite-maturity debt with contractual coupon payment c, instantaneous debt retirementrate m, and total principal p, the value of equity in regime i L; H is given by(vL x; c d L x; c; m; p; xXxL ;eL x; c; m; p (37)0;xpxL ;and8v x; c d H x; c; m; p;>< HeH x; c; m; p vH x; c d H x; c; m; p;>: 0;

xXxL ;xH pxpxL ;xpxH ;

(38)

where the endogenous default thresholds xL and xH are reported in Proposition 4 and d i and vi in regime i L; H are given in Propositions 1 and 2, respectively.The expressions in Proposition 3 for the value of equity are similar to those for rmvalue (Proposition 2) and, thus, admit a similar interpretation. Since debt and rm valuefunctions individually satisfy the appropriate value-matching conditions in Eqs. (14)(15)and Eqs. (29)(30), equity value, or vi d i , also satises the corresponding valuematching conditions. Likewise, because the debt and rm value functions are derivedbased upon the appropriate continuity and smoothness conditions in Eqs. (16)(17) andEqs. (31)(32),), equity value satises boundary conditions of this type too. Given theabandonment value function of the rm, equity value equals zero in case of both smoothand sudden default when the absolute priority rule is enforced (see Morellec, 2001). Themain difference between rm (or debt) and equity is that the default threshold isdetermined by shareholders and, hence, only depends on equity value.3.3.2. Default policyOnce debt has been issued, the shareholders only decision in the static model is to selectthe default policy that maximizes the value of equity. Within our model, markets arefrictionless and default is triggered by shareholders decision to optimally cease injectingfunds in the rm (see also Leland, 1998; Dufe and Lando, 2001; Morellec, 2004).Formally, an equity value-maximizing default policy in our framework is associated with

where w1 ; w1 ; w2 ; w2 ; B; D; B; and D are given in Eqs. (27)(28) and Eqs. (41)(42), then theequity value-maximizing default policy is characterized by the default thresholds xL RxHand xH that solve the above two equations.As in standard contingent claims models, the default policy that maximizes equity valuebalances the present value of the cash ows that shareholders receive in continuation withthe cash ow that they receive in liquidation. The present value of a perpetual entitlementto the (pre-tax) cash ows to shareholders in state i and at time t is given byK i x c mp=r m. Therefore, for a given debt policy c; m; p, the default thresholdshould decrease with those parameters that increase K i . At the same time, the decision todefault should be hastened by larger opportunity costs of remaining active. Hence thedefault thresholds increase with the debt coupon c and the debt principal p, and decreasewith average debt maturity T 1=m.To better understand the mechanics of default, consider the case of innite maturity debtwhere m 0. In this case, the equity value-maximizing default threshold is linearlyincreasing in the debt service ow c in each regime i (see Appendix B). This default policyimplies that it is possible to represent, for each regime i, the no-default and default regionsas in Fig. 1a. In the no-default region xi ; 1, the value of waiting to default exceeds thedefault payoff and it is optimal for shareholders to inject funds into the rm. In the defaultregion 0; xi , the default payoff exceeds the present value of cash ows in continuationand hence it is optimal for shareholders to default.The region xH ; xL , where default occurs if the value of the aggregate shock changesfrom yH to yL , can then be represented as in Fig. 1b. This gure reveals that while theoptimal default policy corresponds to a trigger policy when the economy is in a boom, thisis not the case when it is in a contraction. In this second state, there are two ways to triggerdefault. First, the value of the idiosyncratic shock can decrease to the default threshold xL .This is the default policy that is described in standard models of the levered rm. Second,there can be a change in the value of the aggregate shock from yH to yL while the value ofthe idiosyncratic shock belongs to the region xH ; xL . We show below that these two waysto trigger default have different implications at the aggregate level.

Fig. 1. Optimal default policy. (a) Represents the equity value-maximizing default policy for m 0 in each regimei as a function of c. This default policy requires the rm to default on its debt obligations the rst time xt reachesxi . (b) Represents the impact of a change in macroeconomic conditions on the value-maximizing default policy.There exists a region for the state variable x for which a shift from the expansion regime to the contraction regimetriggers default.

4. Empirical predictions4.1. Calibration of parametersThis section examines the empirical predictions of the model for the decision to default,value-maximizing nancing policies, and credit spreads on corporate debt. To determineasset prices and capital structure decisions, we need to select parameter values for theinitial value of the rms assets x0 , the risk free interest rate r, the tax advantage of debt t,the recovery rate ai , the volatility of the rms income s, the growth rate of cash ows m,and the persistence in regimes lL and lH . In what follows, we select parameter values thatroughly reect a typical S&P 500 rm. Table 1 summarizes our parameter choices.Consider rst the parameters governing operating cash ows. We set the initial value ofthese cash ows to x0 1. While this value is arbitrary, we show below that neitheroptimal leverage ratios nor credit spreads at optimal leverage depend on this parameter.The risk free rate is taken from the yield curve on Treasury bonds. The growth rate of cashows has been selected to generate a payout ratio consistent with observed payout ratios.The rms payout ratio reects the sum of the payments to both bondholders andshareholders. Following Huang and Huang (2002), we take the weighted averages betweenthe average dividend yields (4% according to Ibbotson and Associates) and the averagehistorical coupon rate (close to 9%), with weights given by the median leverage ratio ofS&P 500 rms (approximately 20%). In our model, the rms payout ratio in regime i isgiven by 1 txyi tci =vi x; ci , where ci is the coupon payment in regime i. In the basecase, the predicted payout is 2.35% in regime L and 6.85% in regime H. Weighting thosevalues by the fraction of the time spent in each regime gives an average payout ratio of:0:4 2:35 0:6 6:85 5:05%. Similarly, the value of the volatility parameter is chosento match the (leverage-adjusted) asset return volatility of an average S&P 500 rms equityreturn volatility.The tax advantage of debt captures corporate and personal taxes and is set equal tot 0:15. Liquidation costs (in percentage) are dened as the rms going concern valueminus its liquidation value, divided by its going concern value, which is measured by 1 a

within our model. Using this denition, Alderson and Betker (1995) and Gilson (1997)respectively report liquidation costs equal to 36.5% and 45.5% for the median rm in theirsamples. We simply take the average, which is about 40%. This asset recovery rate impliesan expected recovery rate of 50% on debt principal, which is close to the historical averagereported by Hamilton et al. (2003).The maturity of corporate debt is chosen to reect the average maturity of corporatebonds as reported by Barclay and Smith (1995) and Stohs and Mauer (1996). Thus, wetake T 5 in our base case. The persistence parameter values reect the fact thatexpansions are of longer duration than recessions. Importantly, the relative increase in thepresent value of future cash ows following a shift from the contraction regime to theexpansion regimes is equal toAH x AL xr myH yL

20%.AL xlL yH lH yL r myL

(43)

Thus, our base case environment calls for reasonable variations of policy choices acrossregimes. In addition, these input parameter values imply a ratio of the default rate in arecession versus a boom between 5 and 7.5, which is consistent with US historical data asreported by Altman and Brady (2001).Finally, we have reported formulas for asset prices, given a coupon c and a principalvalue p. When debt is rst issued, there is an additional constraint relating the marketvalue of corporate debt to its principal: for a given degree of leverage, the coupon c is set sothat market value d i equals principal value p in regime i L; H.4.2. The decision to defaultWe start by analyzing shareholders default decision. As we show in Section 3, when thedefault decision is endogenous, the default threshold selected by shareholders depends onthe parameters determining the rms environment and there exists one default thresholdper regime. Moreover, default thresholds are countercyclical, leading to higher defaultrates in recessions. In particular, we show in the Appendix that, when m 0, we can writethe default threshold in the expansion regime ascK H xH G,r

Fig. 2. Default thresholds ratio. It plots the ratio R xL =xH , which relates the default thresholds in the tworegimes as a function of the persistence of cash ows in the contraction regime lL . Input parameter values are setas in the base case environment and debt is initially issued in the expansion regime. In addition, we presume thatthe coupon level is c 0:2 and that lL 2 0:1; 0:7.

where G is a positive constant and

Z 1

eru xtu ytu duxt xH ; yt yH .K H xH E

(45)

These equations reveal that shareholders default on the rms debt obligations when thepresent value of future cash ows equals the adjusted opportunity cost of remaining active.The adjustment is made through the factor G, which represents the option value of waitingto default. A similar argument applies to the default decision in the recession regime.Another interesting feature of the optimal default policy is that, because of thepossibility of a regime shift, the default thresholds xL and xH are related to one another.Specically, the equity value-maximizing default strategy is characterized by a differentdefault threshold in each regime. Moreover, because of the possibility of a regime shift,each default threshold takes into account the optimal default threshold in the other regime.This functional dependence is captured by the ratio R of the two default thresholds. Twofactors are essential in determining the magnitude of this ratio: (1) the ratio of cash ows inthe expansion versus contraction regimes yH =yL , and (2) the persistence in regimes lL andlH . In particular, the ratio of the two default thresholds increases with yH =yL . In addition,because the persistence in regimes represents the opportunity cost of defaulting in oneregime versus the other, an increase in li reduces the opportunity cost of defaulting inregime i, and hence narrows the gap between the default thresholds in the two regimes.This effect is illustrated by Fig. 2, which plots the ratio of the two default thresholds as afunction of the persistence parameter in the contraction regime L.Importantly, the two default thresholds xL and xH exceed the default thresholdassociated with a one-regime model that would be calibrated during an expansion (i.e.withlH 0 and yt yH for all tX0).6 This feature of the model is represented in Fig. 3, which6This follows from the following arguments. Let eH x; c denote equity value for the one-regime model withyt yH for all t: Then, equation When the rms operating cash ows are given by Eq. (45) implies thatei x; coeH x; c; i H; L: Thus, the value matching condition implies that 0 ei xi ; coeH xi ; c: Since eH x; c

Default Threshold in Boom

0.8

0.6

0.4

0.2

00

0.2

0.4

0.6

0.8

Debt CouponFig. 3. Default thresholds in the two- vs. one-regime models. It plots the two default thresholds that obtain inour model as well as the default threshold xexp that would obtain in a standard model calibrated in the expansionregime as a function of the coupon payment. The short-dashed line, the long-dashed line, and the solid line,respectively, represent xL , xH , and xexp . Input parameter values are set as in the base case environment. Thecoupon payment varies between zero and one.

plots the selected default thresholds as a function of the coupon payment c. Because theprobability of default is increasing in the default threshold, Fig. 3 implies that the two-regimemodel is associated with estimates of the probability of default that are (1) higher than thoseassociated with the one regime model calibrated in a boom and (2) lower than those associatedwith the one regime model calibrated in a recession. This nding has several importantimplications for nancial institutions. First, as noted by Allen and Saunders (2002), previousmodels overly optimistic estimates of default risk during boom times reinforces the naturaltendency of banks to overlend just at the point in the business cycle that the central bankprefers restraint. Our model shows that by recognizing the impact of macroeconomic cycles,a simple two-regime model can help mitigate this effect. Second, because credit risk modelsalso determine the amount of reserves of capital a bank should hold (and hence the amount ofcapital a bank can allocate to the real side of the economy), our model should also mitigate thecyclical cash constraint effects that show up in the lending process by reducing the estimates ofthe probability of default when the economy is in a recession.While some of the above arguments are familiar from the contingent claims literature,the present model delivers a richer set of default policies than do traditional contingentclaims models. Notably, when the aggregate shock can shift between discrete states atrandom times, default by rms in a common market or industry can arise simultaneously(see also Giesecke, 2002; Driessen, 2005; Cremers et al., 2005). This clustering of defaultswill happen when the idiosyncratic shock of several rms belongs to the transient regionand the aggregate shock shifts from yH to yL (thereby triggering an immediate default ofthese rms). Importantly, in the standard model with a single risk factor, a clustering ofdefaults is unlikely to occur with the sequential exercise of options to default, unless rms(footnote continued)is increasing in x; it follows that the default threshold for the one regime model with yt yH must be lower thanxi : Similarly, one can show that the default threshold for the one regime model with yt yL is higher than xi :

are identical. However, a standard diffusion model with stochastic volatility as a secondaggregate risk factor could also be used to model joint defaults. In our model the aggregaterisk factor can only take two values, and hence implies a common systemic jump todefault.4.3. Optimal leverage and debt capacityWe now turn to the analysis of leverage decisions. Within our setting, the leverage ratiois dened byLi x; c; m; p

d i x; c; m; p;vi x; c

i L; H.

(46)

While default policy is selected by shareholders to maximize equity after the issuance ofcorporate debt (and hence maximizes ei ), debt policy maximizes ei plus the proceedsfrom the debt issue, i.e. vi ei d i for i L; H. Because rm value depends on thecurrent regime, the selected coupon rate and leverage ratio also depend on the currentregime. The coupon rate selected by shareholders is the solution to the problem:maxc vi x; c. Denote the solution to this problem by ci x. We assume that this solution isunique and verify this conjecture in the simulations. Optimal leverage then equalsLi x; m; p Li x; ci x; m; p. In the simulations below we compute optimal leverageassuming that the recovery rate does not depend on the regime.In the base case environment, the value-maximizing leverage ratio is equal to 19.72% ina recession and 16.61% in a boom. Thus, within our model, leverage is countercyclical.This feature of the model is consistent with the evidence reported by Korajczyk and Levy(2003). The countercyclical nature of leverage results from two countervailing effects.First, regime shifts affect the rms default risk. Second, regime shifts change the presentvalue of future cash ows. In particular, the coupon rate, which determines the book valueof debt, in the expansion regime exceeds the coupon rate in the contraction regime,reecting the additional debt capacity associated with a lower default risk. At the sametime, however, the present value of future cash ows is greater in the expansion regime,increasing the denominator of Eq. (46). In our model, the second effect always dominatesthe rst, generating the countercyclicality in leverage.7 Importantly, the fact that thecoupon is regime dependent alleviates somewhat the difference between default thresholdsand debt capacities in booms versus recessions (see below).Because rm value depends on the various dimensions of the rms environment, so doesthe leverage ratio selected by shareholders. Consider, for example, the impact of volatilityon the rm value-maximizing leverage ratio. In contingent claims models of the leveredrm, the volatility parameter provides a measure of bankruptcy risk. This in turn impliesthat this parameter affects both expected bankruptcy costs and the tax advantage of debt the greater volatility, the shorter the time period over which the rm benets from the taxshield. Since optimal capital structure reects a trade-off between these two quantities(recall that in our model investment policy is xed), optimal leverage depends crucially onthe level of the volatility parameter. In particular, an increase in volatility typically raises7Given that we assume the default-riskfree interest rate is constant, it would be potentially interesting, buttechnically challenging, to extend our regime-switching model to procyclical variations in interest rates.Inutitively, a procyclical interest rate process should attenuate the present value effect.

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Table 2

Bases 0:20s 0:30lL 0:10lL 0:20T 3T 7

Contractioncoupon

Regimeleverage

Expansioncoupon

Regimeleverage

0.11960.15130.09580.10640.12890.09100.1453

19.7224.9715.7019.9119.5715.3123.39

0.12060.15230.09670.10820.12950.09130.1473

16.6121.0313.2415.9817.0212.8319.83

default risk and hence reduces the value-maximizing debt ratio. Table 2 providescomparative statics that show the impact of volatility on the quantities of interest.Data in Table 2 and Fig. 4 reveal that the selected coupon rate and leverage ratio arevery sensitive to the values of the volatility parameter. For example, as volatility increasesfrom 20% to 30%, optimal leverage in the expansion regime decreases from 21.03%to 13.24%.Consider next the impact of persistence in regimes on nancing decisions. Numericalresults in Table 2 indicate that the persistence in regimes is an important determinant ofvalue-maximizing nancing policies. For example, as lL , an indicator of the nonpersistence of regime L, increases from 0.1 to 0.2, it is optimal for shareholders to increasethe optimal coupon payment in regime L by 21% (from 0.1064 to 0.1289). Data in Table 2and Fig. 4 also reveal that an increase in li decreases optimal leverage since rm value itselfdepends on persistence in regimes. Because of the very nature of the model, a change in liaffects quantities in both regimes. Maturity also has a signicant impact on nancingdecisions. In our model, a reduction in the maturity of the debt contract implies an increasein the debt service and thus an increase in the probability of default. The optimal responsefor the rm is to issue less debt. Simulation results reported in Table 2 show for examplethat as the average debt maturity T decreases from seven to three years, the rm optimallyreduces its leverage ratio from 19.8% to 12.8% in the expansion regime. Finally, and asillustrated by Fig. 4, other standard comparative statics apply within our model, so we donot report them.An alternative expression for the variations in debt policy that may arise because ofchanges in macroeconomic conditions relates to their impact on the rms debt capacity. Inthis paper, we dene debt capacity as the maximum amount of debt that can be soldagainst the rms assets. Arguably, if default clusters can arise in a recession, the expectedrecovery rate on the rms assets is likely to be lower than the expected recovery rate in aboom since the industry peers are likely to be experiencing problems themselves (seeShleifer and Vishny (1992) for a theoretical argument and Acharya et al. (2003) forevidence). Thus, we report in Fig. 5 the debt capacity of the rm for different recoveryrates in a recession. Because default risk is lower in an expansion than in a contraction, thedebt capacity of the rm is greater when the economy is in an expansion. In the base caseenvironment for example, the maximum value of corporate debt that could be sold in aboom is 15% larger than the maximum value that could be sold in a contraction. As therecovery rate in the contraction regime decreases, this difference between regimes increasesand exceeds 40% when aL 0:2.

Fig. 4. Optimal leverage ratios. It plots the optimal leverage ratio of the rm as a function of: (1) the growth rateof cash ows m; (2) the volatility of cash ows s; (3) the persistence of recessions lL ; and (4) the recovery rate aH .The solid line represents optimal leverage in a boom and the dashed line optimal leverage in a recession. (a)Leverage and growth rate. (b) Leverage and volatility. (c) Leverage and persistence. (d) Leverage and recoveryrate.

1.5

Debt Capacity Ratio

1.41.31.21.110.2

0.3

0.50.60.4Recovery Rate in Recession

0.7

0.8

Fig. 5. Debt capacity. It plots the ratio of the debt capacity in a boom to the debt capacity in a contraction as afunction of the recovery rate in the contraction regime. Debt capacity is dened as the maximum amount of debtthat the rm can oat.

Credit Spreads in Boom

7006005004003002001000

10Debt Maturity

10Debt Maturity

(a)

15

20

Credit Spreads in Recession

7006005004003002001000(b)

15

20

Fig. 6. Term structure of credit spreads. (a) and (b) plot the term structure credit spreads on corporate debt. Theve lines represent credit spreads resulting from leverage ratios of 30%, 40%, 50%, 60%, and 70% in a boom. Weuse the same debt structure c; m; p to compute spreads in a recession. (a) Term structure of credit spreads in aboom. (b) Term structure of credit spreads in a recession.

4.4. Term structure of credit spreads

We now turn to the analysis of credit spreads on corporate debt. Credit spreads onnewly issued debt are measured by the following expression:csi x; c; m; p

c r.d i x; c; m; p

(47)

Fig. 6 examines the credit spread on newly issued debt as a function of average debtmaturity T, for alternative leverage ratios when the recovery rate does not depend on theregime. For highly levered rms, credit spreads are high, but decrease as the average debtmaturity T increases beyond one year. For medium-to-high leverage ratios, credit spreadsare hump-shaped. That is, intermediate-term debt promises higher yields than either shortor long-term corporate debt. Credit spreads of low leverage rms are low, but increase withmaturity T.In contrast to previous contingent claims models, our framework can produce nontrivial credit spreads for short-term corporate debt issues (see also Dufe and Lando, 2001;Zhou, 2001). In the base case environment, credit spreads are relatively close to zero for

short-term debt when the economy is in a boom. However, in a recession very short-termcredit spreads taper off at around 20200 basis points in case of medium to high leverage.As a result, the slope of the term structure is steeper at the short end in booms than inrecessions. This result obtains because with regime shifts investors are always moreuncertain about the nearness of default. The gure also reveals that in a recession, creditspreads on debt exceed those prevailing during a boom by up to 150 basis points.Let us now turn to analyzing the determinants of credit spreads. Consider rst volatility.Fig. 7 indicates that credit spreads increase with the volatility of cash ows from assets inplace. Within the present model, volatility has two effects on credit spreads. First, for agiven coupon payment, the probability of default and, hence the cost of debt, increaseswith the volatility parameter s. Second, because the cost of debt increases with s, theoptimal response for shareholders typically is to issue less debt. Numerical results indicatethat the rst effect dominates, so that credit spreads increase with volatility.Consider next the growth rate of cash ows. Again, the impact of this parameter oncredit spreads at optimal leverage results from two opposite effects. First, for a givencoupon payment, the default threshold selected by shareholders decreases with m and so doexpected bankruptcy costs. Second, because the cost of debt decreases with m, it is optimalfor shareholders to issue more debt. Numerical results reported in Fig. 7 indicate that therst effect dominates so that credit spreads decrease with the growth rate of cash ows.Numerical results also reveal that, because lower recovery rates imply a lower leverage

5. Dynamic capital structure

In this section, we extend the basic model to allow for dynamic capital structure choice.To simplify the analysis, we presume throughout the section that m 0. In addition, wefollow Fries et al. (1997) and Goldstein et al. (2001) by considering that the rm can onlyadjust its capital structure upwards.8 Specically, we presume that there exists twoUUUthresholds xUH and xL , xL 4xH , such that the rm increases its coupon payment onceUoperating cash ows reach yi xi in regime i. We also assume that whenever the rm issuesdebt, it incurs a proportional otation cost i.The scaling feature underlying our model permits the adoption of the dynamic capitalstructure formulation developed by Leland (1998) and Goldstein et al. (2001). To see this,observe that when m 0, the default thresholds xH and xL are linear in c. In addition, theoptimal coupon rates cH and cL are also linear in x.9 This implies that if two rms A and Bare identical except that their initial values of idiosyncratic shocks differ by a factorBAxB0 ri xA0 in regime i H; L, then the optimal coupon rate in regime i, ci ri ci , theBAoptimal default threshold, xi ri xi , and every claim in regime i will be larger by thesame factor ri . For the dynamic model, the scaling feature implies that since at the time ofa restructuring the value of the idiosyncratic shock in regime i; xU1 ri x0 ; is a factor riiD0larger than its time 0 initial level x0 , it will be optimal to choose c1i ri c0i , xD1i ri xi , andU1U0xi ri xi , and all claims in regime i will scale upward by the factor ri .We now use this scaling property of the model to solve for optimal dynamic capitalstructure. In our model rm value is equal to the value of unlevered assets plus the taxbenet of debt minus bankruptcy and otation costs. Thus, we can write the value of therm in regime i as:vi x; c Ai x TBi x; c BC i x; c IC i x; c iPi ,

(48)

where TBi x; c is the total tax benet in regime i, BC i x; c are the total expectedbankruptcy costs in regime i, iPi are the initial otation costs in regime i, and IC i x; c isthe present value of the otation costs paid by the rm when restructuring its capitalstructure. Similarly, we can write the value of equity in regime i as ei x; c vi x; c Di x; c, where Di x; c is the value of debt in regime i. The default threshold8

The analysis can be extended to incorporate nite maturity debt and downward restructurings along the linesof Leland (1998). As discussed in Goldstein et al. (2001), while in theory management can both increase anddecrease future debt levels, Gilson (1997) nds that transaction costs discourage debt reductions outside ofChapter 11. In addition, the fact that equity prices tend to trend upwards makes the option to issue additionaldebt more valuable than the option to repurchase outstanding debt. Finally, in this model (as in Leland, 1998),increasing maturity always increases rm value by increasing its debt capacity. Hence the optimal policy is to issueinnite maturity debt, i.e., to set m 0.9This follows from the following arguments. Eqs. (B.3)(B.6) in the Appendix imply that A c1x A0 ; B c1g B0 ; C c1b1 C 0 ; D c1b2 D0 ; where A0 ; B0 ; C 0 ; and D0 are independent of c. Thus, Eqs. (B.1)(B.2) imply thateH and eL are homogeneous of degree one in x and c: Similarly, debt values d H and d L are homogeneous of degreeone in x and c. This in turn implies that rm value has this homogeneity property in regime i H; L: Therefore,the optimal coupon rate in regime i is linear in x:

selected by shareholders in regime i satises the smooth-pasting condition

e0i xi ; c 0,

(49)

where derivatives are taken with respect to x. Shareholders objective is then to chooseci ; ri xUi =x0 to maximize rm value subject to the above smooth-pasting condition andthe requirement that debt is issued at par. That is, we allow the rm to choose differentnancing and restructuring strategies depending on the prevailing regime.We report in Table 3 numerical results that rely on the solution presented in Appendix Cwhen the value of the aggregate shock is yH (i.e., the expansion regime). As in Section 4,similar results with lower coupon payments and higher leverage ratios obtain in thecontraction regime. Table 3 illustrates the following features of the dynamic model.First, the possibility to adjust capital structure dynamically increases rm value and theassociated gain decreases with the magnitude of otation costs, as suggested by economicintuition. While the potential gain reported in Table 3 is low, this essentially results from alow tax benet of debt in our base case environment. As the tax benet of debt increases,the potential increase in rm value rises. For example, when the marginal corporate taxrate is 35% and otation costs are 1%, the value of the unlevered rm is 9.8, the value of alevered rm following a static capital structure policy is 11.15, and the value of a leveredrm following a dynamic capital structure policy is 11.73. Thus, the possibility of issuingdebt increases rm value by 14% in the static model and by 20% in the dynamic model,compared with an unlevered rm.A second interesting feature of the results reported in Table 3 is that the defaultthresholds in the dynamic model are always lower than the default thresholds in the staticmodel. This feature results from two separate effects. First, the debt policy of the rm ismore conservative in the dynamic model and thus the opportunity cost of remaining activeis lower. Second, because of the options to increase leverage in the future, rm value ismore valuable and it is thus optimal for shareholders to postpone the decision to default.The third interesting feature of the data reported in Table 3 is that, consistent witheconomic intuition, the restructuring thresholds increase with otation costs. In addition,because the tax advantage of debt is greater when yt yH than when yt yL , theUrestructuring thresholds satisfy xUH oxL . This result has several implications. First, itimplies that rms should adjust their capital structure more often in booms than inrecessions since the expected time between restructurings is decreasing with the value of therestructuring threshold. Second, it also implies that, holding investment policy xed, rmsshould adjust their capital structure by smaller amounts in booms than in recessions.10Indeed, suppose that the rm makes its initial nancing decision when the economy is in anexpansion and selects the coupon level c0H . Then, if the process x rst reaches xUH in aboom, the rm raises debt so that its new coupon is c1H c0H xU=x.Iftheprocessx rst0Hreaches xUinarecession,thenthermraisesalargerdebtamountsothatitsnewcouponL1is c0H xUL =x0 4cH . If the rm is in a recession regime when making its rst nancing10

Drobetz and Wanzenried (2004) use a dynamic adjustment model and panel methodology to provide a directtest of this hypothesis on a sample of 90 Swiss rms over the 19912001 period. Basing their tests on the dynamicpanel data estimator suggested by Arrelano and Bond (1991), Drobetz and Wanzenried demonstrate that thespeed of adjustment toward optimal capital structure depends on the stage of the business cycle. In particular,they demonstrate using popular business cycle variables that the speed of adjustment to the target is faster wheneconomic prospects are better.

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Table 3Expansion

i0.001

0.005

0.01

0.015

Dynamicmodel

Firm valueLeverageCouponxUHxULxDHxDL

13.3525.960.2481.431.490.110.16

13.3027.700.2621.871.960.120.17

13.2528.370.2642.252.350.120.17

13.2028.510.2652.592.700.170.17

Staticmodel

Firm valueLeverageCredit spreadsxUHxULxDHxDL

13.0736.24162NANA0.160.23

13.0635.64159NANA0.160.22

13.0434.87154NANA0.150.21

13.0134.06150NANA0.140.20

decision, then the rm issues an initial debt contract with a smaller coupon c0L and theabove argument goes through with c0L replacing c0H .Finally, it should be noted that the rms optimal leverage ratio is lower in the dynamicmodel than in the static model. This is due to the fact that we only consider the possibilityof increasing leverage in the future (a similar point is made in Goldstein et al., 2001). Whenboth upward and downward leverage adjustments are allowed, the leverage ratio in thedynamic model is closer to that of the static model. It should also be noted that in thedynamic model leverage increases with otation costs while in the static model leveragedecreases with otation costs. The latter effect results from the greater costs of issuing debtthat reduces optimal leverage in the static model. The former effect is due to the fact that asadjustment costs increase, the optimality (and likelihood) of future changes in leveragedecreases. Thus, the optimal response for the rm is to issue an amount of debt that iscloser to that of the static case.6. ConclusionWhen operating cash ows depend on current economic conditions, rms should adjusttheir policy choices to economys business cycle phase. While this basic point has alreadybeen recognized, its implications have not been fully developed. In this paper, we present acontingent claims model of the levered rm, where operating cash ows depend on therealization of both an idiosyncratic and an aggregate shock (that reects the state of theeconomy). With this model, we show that:(1) When the aggregate shock can shift between different states, shareholders optimaldefault policy is characterized by a different threshold for each state and defaultthresholds are countercyclical, leading to higher default rates in recessions. Moreover,

because the states are related to one another, the value-maximizing default policy ineach state reects the possibility for the rm to default in the other states.Under this policy, default can be triggered either because the idiosyncratic shock hasreached the default threshold in a given regime or because of a change in the value ofthe aggregate shock. As we argue in the paper, the rst type of default-triggering eventis unlikely to explain the clustering of exit decisions observed in many markets. Bycontrast, the second type provides a rationale for such phenomena.The leverage ratios that the model generates are in line with the leverage ratiosobserved in practice. In addition, the model predicts that market leverageshould be countercyclical, consistent with the evidence reported by Korajczyk andLevy (2003).The credit spreads generated by the model are in line with those observed in practice.For any given debt level, credit spreads are higher in a recession than in a boom. Thechange in credit spreads following a change in the value of the aggregate shock can besubstantial, reaching up to 120 basis points for nancially distressed rms. In addition,the term structure of credit spreads produced by the model encompasses potentiallysubstantial short term credit spreads.As Shleifer and Vishny (1992) conjecture, the rms debt capacity depends on currenteconomic conditions. Firms typically will be able to borrow more funds in a boom,even assuming a constant loss given default. If the recovery rate is procyclical, the debtcapacity of the rm in a boom can be up to 40% larger than the debt capacity of thatsame rm in a contraction.When the rm can adjust its capital structure dynamically, both the pace and the size ofthe adjustments depend on current economic conditions. In particular, rms shouldadjust their capital structure more often and by smaller amounts in booms than inrecessions.

While our model generates implications that are consistent with the available empiricalevidence, it also provides a basis for future empirical work. In particular, while there issome evidence that rms nancing decisions are regime dependent, there is relatively littlework on the pace and size of capital structure changes across business cycle regimes.Huang and Ritter (2004) nd using CRSP and Compustat data that real GDP growth ispositively associated with the likelihood of debt issuance, but is not reliably related to thelikelihood of equity issuance. Drobetz and Wanzenried (2004) provide a direct test of ourpredictions on the pace of capital structure changes on a sample of 91 Swiss rms.Consistent with our hypothesis, they nd that macroeconomic conditions affect the speedof adjustment to target leverage. In particular, the speed of adjustment is higher when theterm spread is higher, i.e., when economic prospects are good. Finally, de Haas and Peeters(2004) also nd that higher GDP growth increases the adjustment speed [to target capitalstructure] in Estonia, Lithuania, and Bulgaria. More generally, empirical work on thistopic using larger data sets is called for. We leave this issue for future research.

Appendix A. Finite maturity debt value

To solve the system of ODEs (12)(13), dene the following functions: g d H d Land h lL d H lH d L . We then have the following system of equations on the

Appendix C. Dynamic capital structure

In this section we allow the rm to adjust its capital structure upwards. We assume thatin the case of a restructuring, the debt is called at par: Di xUi ; c Pi . Under thisassumption, the value of corporate debt satises the set of ODEs:

The boundary conditions associated with this system of equations are given byDi xUi Pi ;Di xDi

i L; H,

C:5

ai Ai xDi ;

i L; H,lim DL x lim DL x,

C:6C:7

lim D0L x lim D0L x,

C:8

lim DH x lim DH x,

C:9

lim D0H x lim D0H x.

C:10

x#xUHx#xUHx#xDLx#xDL

x"xUHx"xUH

x"xDLx"xDL

Similarly, tax benets are akin to a security (1) that pays a constant coupon tc as long asthe rm is solvent and (2) whose value is scaled by a factor ri in regime i at the time of therestructuring. Thus, tax benets satisfy the system of ODEs: